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We study the bidirectional lightwave propagations in an erbium-doped fiber ring laser and an inverted-S fiber ring laser, and observe their optical bistability behaviors. We develop a model for the inverted-S fiber ring laser using nonlinear optical loop mirror and nonlinear amplifying loop mirror (NOLM-NALM) principle, which operates in the nonlinear region. Good agreements between the laser experimental performance and the developed model are achieved. The laser shows good switching and pulse compression capabilities. In addition, the laser model illustrates the route to chaotic operation via period doubling bifurcation, when the input power increases. We also obtain quasi-periodic operation when the laser is amplitude modulated experimentally.